
from collections import defaultdict
from math import ceil, sqrt

def 		UpperCamelCase						(   lowercase_ = 1_00_00_00			,			lowercase_ = 10 )		->						int:


  '''simple docstring'''






  lowercase__	: defaultdict     		=   defaultdict(lowercase_ )

  for outer_width in range(3			,			(t_limit // 4) + 2 ):
    if outer_width * outer_width > t_limit:
      lowercase__	: Any     		=   max(
          ceil(sqrt(outer_width * outer_width - t_limit ) )			,			1 )
    else:
      lowercase__	: List[str]     		=   1

    hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

    for hole_width in range(lowercase_			,			outer_width - 1			,			2 ):
      count[outer_width * outer_width - hole_width * hole_width] += 1

  return sum(1 for n in count.values() if 1 <= n <= 10 )


if __name__ == "__main__":
     print(f'''{solution() = }''')














'''simple docstring'''







def       __UpperCamelCase					(      lowercase_       :  list[int]   ,       lowercase_       :  list[int]   ,       lowercase_       :  int   ):
       """simple docstring"""




       return not any(
           neighbour == 1 and colored_vertices[i] == color
           for i, neighbour in enumerate(lowercase_   )   )


def       __UpperCamelCase					(      lowercase_       :  list[list[int]]   ,       lowercase_       :  int   ,       lowercase_       :  list[int]   ,       lowercase_       :  int   ):
       """simple docstring"""




       if index == len(lowercase_   ):
              return True

       # Recursive Step
       for i in range(lowercase_   ):
              if valid_coloring(graph[index]   ,       lowercase_   ,       lowercase_   ):
                     # Color current vertex
                     a_						     =			i
                     # Validate coloring
                     if util_color(lowercase_   ,       lowercase_   ,       lowercase_   ,       index + 1   ):
                            return True
                     # Backtrack
                     a_						     =			-1
       return False


def       __UpperCamelCase					(      lowercase_       :  list[list[int]]   ,       lowercase_       :  int   ):
       """simple docstring"""




       a_						     =			[-1] * len(lowercase_   )

       if util_color(lowercase_   ,       lowercase_   ,       lowercase_   ,       0   ):
              return colored_vertices

       return []




